Quantifying environmental and other detrimental risks from exposure to hazardous agents is an important component in the process of risk evaluation and assessment. The primary goal of this project is to develop and study methods of simultaneous statistical inference for use in low-dose risk extrapolation. Application is directed to environmental and occupational risk assessment studies where human or animal data are used to set benchmark or other safe low-dose levels of a hazardous agent, but where study information is limited to high dose levels of the agent. Methods are emphasized for simultaneous upper confidence limits on predicted risk for proportion endpoints. From the simultaneous bounds, lower confidence limits on the benchmark dose (BMD) associated with a particular risk are calculated. An important feature of the simultaneous construction is that any inferences based on inverting the simultaneous confidence bounds apply automatically to inverse bounds on the BMD. The methodology extends previous results for simultaneous confidence bands to binomial and overdispersed proportion data under a series of link functions that describe the dose-response relationship. Consideration is also given to address model selection bias across the various link functions via computerized model adequacy appraisals. An evaluation phase of the project studies the small-sample operating characteristics of the methodology via Monte Carlo computer calculations. The new methods continue to fill existing gaps in low-dose risk extrapolation, and have application to the important problem of performing low-dose risk assessment with proportion data. World Wide Web software is constructed to allow the methods to be accessible to the widest possible corps of users.